Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
Correct Answer
$8720
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5450 × 6% × 10
= $5450 ×6/100 × 10
= 5450 × 6 × 10/100
= 32700 × 10/100
= 327000/100
= $3270
Thus, Simple Interest = $3270
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3270
= $8720
Thus, Amount to be paid = $8720 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5450
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 6% × 10)
= $5450 + ($5450 ×6/100 × 10)
= $5450 + (5450 × 6 × 10/100)
= $5450 + (32700 × 10/100)
= $5450 + (327000/100)
= $5450 + $3270 = $8720
Thus, Amount (A) to be paid = $8720 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5450, the simple interest in 1 year
= 6/100 × 5450
= 6 × 5450/100
= 32700/100 = $327
Thus, simple interest for 1 year = $327
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $327 × 10 = $3270
Thus, Simple Interest (SI) = $3270
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3270
= $8720
Thus, Amount to be paid = $8720 Answer
Similar Questions
(1) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?
(5) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(6) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.
(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?
(10) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.